Tuesday, September 30, 2008

Autistic Time Lines

My autistic son's sixth grade English teacher is insisting that he redo the "First Five Years of My Life Timeline" he created for this month's "All about Me" unit.

The problem?  The events he included:
November, 1999:  I thought the porch fan switch was broken.
June, 2001: I realized that Mommy was only pretending the switch was broken so I wouldn't keep turning it on and off.
September, 2001:  Porch fan switch actually broke.
May, 2002:  Porch fan switch fixed.
I tried to tell her that J did this assignment in good faith, and that these really were among his most memorable milestones. 

"The assignment doesn't meet expectations," she insisted.  

One of the ironies here is in the premise behind such narcissistic units as "All about Me:"

Students learn best when relating things to their personal interests.

Apparently only the personal interests of neurotypical children count, and what is supposed to be an alluring tie-in for most students becomes a major obstacle for those with autism.

Sunday, September 28, 2008

Autism Diaries, II: a universe far, far away

Step one:  Set up a gmail account in your babysitter's name.

Step two:  From that account, email her the following message:
You & I have a same first name, same middle name, and same last name. My life is same as yours. I babysit "J" [His name] like you. I look like you. I babysit different "J". I live in different universe which is quadrillion light years away from you. I have a special computer internet which radio ways are quadrillion light years per second.
The least plausible claim in this email message is that there's anyone anywhere else in the universe like "J".

Friday, September 26, 2008

Math problem of the week: 4th grade Trailblazers vs. Singapore Math

1. From 2/3 of the way through the grade 4 Math Trailblazers workbook, p. 144:

A. When Shannon and her family arrived at the park on Saturday, Shanon counted 3 children on each of the following: the slide, the swings the monkey bars, and the merry-go-round. How many children were at the park when Shannon arrived?

B. If there were 8 more children than adults at the park, how many adults were at the park?

...

Shannon treated her little sister and her mother to a treat. At a nearby stand she bought two cans of juice at 65c each and three popsicles at 85c each. She gave the vendor $5.00. How much change will Shannon receive?

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2. From 2/3 of the way through the grade 4 Singapore workbooks, Primary Mathematics 4b, p. 120

A computer costs $2290.  An oven costs 1/5 the cost of the computer.  How much more does the computer cost than the oven?

A basket, together with 6 cans of mushrooms, weighs 3.05 lb.  Each can of mushrooms weighs .43 lb. Find the weight of the basket when it is empty.


---------------

OILF's Assessment

In the first Trailblazers problem, the italic each gives away the multiplication operation, and the problem is split into two parts so you know to multiply first, then add--unlike the Singapore problems, where you have to figure out which operations to use, and in what order.

Both Trailblazers problems stick to friendly numbers:  2, 3, 4, 5, 8, 65 and 85.  Their Singaporean counterparts, meanwhile, use a four digit number, a fraction, and two unfriendly decimals.

Playgrounds and refreshments vs. major appliances.

Tuesday, September 23, 2008

Eliminating the SAT: disadvantaging the left-brainers

A commission convened by some of the country’s most influential college admissions officials is recommending that colleges and universities move away from their reliance on SAT and ACT scores and shift toward admissions exams more closely tied to the high school curriculum and achievement.
So reports yesterday's New York Times.

The commission, convened by the National Association for College Admission Counseling, cites three concerns.  In the words of study leader William R. Fitzsimmons,  the dean of admissions and financial aid at Harvard University:

(1) "test scores appear to calcify differences based on class, race/ethnicity and parental educational attainment."

(3) "the contrast between opportunities and fancy suburbs and some of the high schools that aren’t so fancy"

(3) "academic research that suggests that test preparation and coaching results in an increase of 20 to 30 points on the SAT"

As a result of such concerns, the Times writes:
A growing number of colleges and universities, like Bates College in Maine, Lawrence University in Wisconsin, Wake Forest University in North Carolina and Smith College in Massachusetts, have made the SAT and ACT optional. And the report concludes that more institutions could make admissions decisions without requiring the SAT and ACT.
Indeed:
More than 280 four-year colleges do not require standardized test scores for admission, according to the study.
According to Mr. Fitzsimmons, Harvard may be next.

The report's recommendations:

1. Institutions should "consider dropping admission test requirements unless they can prove that the benefits of such tests outweigh the negatives."

2. "what is needed is a new achievement test, pitched to a broad group of students, that would predict college grades as well as or better than available tests."

Such an achievement test, the report claims, would (quoting the Times quoting the report):
“encourage high schools to broaden and improve curricula,” and would also send a message to students to focus on their high school course material instead of on test preparation courses.
-----
OILF's concerns:

Re the new achievement test:

1. The original point of the SATs was to open up college admissions to students who didn't come from fancy schools and who were thereby disadvantaged in subject-area college admissions tests.  Why would replacing the SATs with a new achievement test make things any more equitable?  To the extent that the proposed new test encourages the weaker high schools "to broaden and improve curricula," such changes take years, if not decades, to put into place, let alone to trickle down to actual students.

2. The influence may just as likely go in the other direction, with the power brokers in the education establishment, rather than reforming the schools, retrofitting the new achievement test--with all the predictable results.  E.g.: assessing students not on doing hard math and science, but on how well they communicate about math and science.

Re assigning greater weight to grades: 

1. As I've argued here, here, here, here, here, here, here, here, and here the latest pedagogical priorities have made it harder and harder for even--and sometimes especially--the smartest left-brainers to earn good grades.

2. For such students, the SAT is increasingly the one recourse for distinguishing themselves academically and, therefore, for gaining admission to selective colleges.

Sunday, September 21, 2008

Right-brained foreign language assignments: the German tissue box

When I learned, this weekend, that my nephew had to decorate a tissue box for German class, I was curious whether this was the brainchild of his particular teacher, or a general trend in German language instruction.

I googled "tissue box" "German," and found three links touting my nephew's assignment:




Note, especially, the grading rubric, with its ratings for creativity and craftsmanship.

I find myself brimming over with questions as I peruse these sites; perhaps the most burning one of all is this:

When will this contagious meme (to use Richard Dawkins' term), this sticky idea (to use Malcolm Gladwell's term), this creative, crafty pedagogical epiphany, catch on in other Germanic language classrooms--like Swedish and Dutch?

Who knows, it might even liven up French, Russian, and Chinese.

Thursday, September 18, 2008

Math problem of the week: 2nd grade Investigations vs. Singapore Math

1. From the beginning of the grade 2 Investigations curriculum (Counting, Coins, and Combinations, Family Letter about Benchmarks/Goals):

7 + 3 = 5 + 1 = 5 + 2 =
6 + 4 = 6 + 1 = 2 + 8 =
5 + 5 = 1 + 9 = 2 + 7 =

2. From the beginning of the grade 2 Singapore Math curriculum (Primary Mathematics 2B, p. 13)

1 more than 76 is
1 less than 76 is
10 more than 72 is
10 less than 76 is

2 more than 76 is
2 more than 76 is
20 more than 76 is
20 less than 76 is

2 more than 38 is
10 more than 63 is
20 more than 80 is
2 less than 75 is
10 less than 86 is
20 less than 94 is

-----
Extra Credit: 

Which problems does your 7-year-old find most challenging?  Most interesting?

Wednesday, September 17, 2008

Please visit an actual classroom before you make recommendations, III

This time the recommendations come from Natalie Angier, a science reporter with the New York Times.

In this week's Science Section, she reports on two studies showing connections between two cognitive number mechanisms:

1. The approximate number system: in Angier's words, "an ancient and intuitive sense that we are born with and that we share with many other animals."

2. The abstract, symbolic system that allows us to "manipulate representations of numbers" and make precise calculations.

One study shows that a person's facility with the approximate system is connected to his/her facility with the symbolic system. The other shows that, in Angier's words:

[P]reschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific.
All this, Angier reports, has "potentially broad implications for math education:"
Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.
Huh? Less on symbolic and more on approximate? This is a non-sequitor, unless we know that the causality flows from approximate to symbolic.

But as Angier quotes one of the researchers (Lisa Feigenson of Johns Hopkins) as saying, “We can’t draw causal arrows one way or another" between "your evolutionarily endowed sense of approximation" and "how good you are at formal math.”

And, as Angier herself writes: "The researchers caution that they have no idea yet how the two number systems interact," and that it's currently an "open question[] ...how malleable our inborn number sense may be, whether it can be improved with training, and whether those improvements would pay off in a greater appetite and aptitude for math."

So how does Angier leap to the conclusion that schools should be stressing approximate number sense over symbolic numerical reasoning?

It seems that our science reporter has managed to:

1. avoid visiting actual classrooms, where she would see how much symbolic math has been jettisoned the sake of "number sense," and by how much overall levels of math achievement have therefore declined.

2. fall under the influence of the reigning ed school orthodoxy, which is as enamored of intuition as it is contemptuous of abstract reasoning.

3. take, on faith, the bizarre claims by one of the researchers about the parlor games played by mathematicians:
“When mathematicians and physicists are left alone in a room, one of the games they’ll play is called a Fermi problem, in which they try to figure out the approximate answer to an arbitrary problem,” said Rebecca Saxe, a cognitive neuroscientist at the Massachusetts Institute of Technology who is married to a physicist. “They’ll ask, how many piano tuners are there in Chicago, or what contribution to the ocean’s temperature do fish make, and they’ll try to come up with a plausible answer.”
Not the mathematicians I know!

Why doesn't anyone ask them about what they think of what's going on in today's actual classrooms?

Sunday, September 14, 2008

Reform Science and the fate of the science experiment

"It's not as if I have the kids go in and do a science experiment, and then go in the next day and do another experiment, and so on.." my son's 6th grade science teacher told me.

Rather, he assured, today's science classes focus on more important things, like communicating scientific ideas through presentations and posters.

The science experiment is now an optional home venture: the fourth and final option on the weekly homework sheet, listed after (1) the calculator-facilitated metric conversion worksheet, (2) the calculator-facilitated area & volume worksheet, and (3) the communications assignment (pick a science article, summarize it, and write a personal reflection of what you thought about it).

And the experiment's instructions are so imprecise that it's not clear what you're actually supposed to be doing or testing out.

The question:

Does the amount of salt in water affect the amount of freshwater produced?
"Produced"?

In one trivial sense, the answer is yes. Any significant amount of salt reduces the amount of freshwater down to zero, because when you add enough salt to freshwater it's no longer fresh.

In another trivial sense, the answer is no: adding substance B to substance A doesn't subtract from substance A.

Whatever. Maybe the directions will somehow illuminate matters:
Mix salt and water to make salt water.
Do the proportions matter? A sprinkling of salt? A whole ladel full?
Add about 2 inches of the water to a pot.
But remember the area and volume sheet! Inches are linear! What on earth is "2 inches of water"?
Put an empty glass in the bowl.
Just "put?" Centered? On its side? Upside down?
Seal plastic wrap over the top, weigh it down with a rock (centered above the bowl?)... Now you've made a solar still.
Oh, OK. Let's re-position the cup accordingly.

But what if no one at home knows what a solar still is already?
Repeat with fresh water.
"Two inches" of water?

In a pot the same size as the first? Actually, it's a good thing this is left unspecified: we don't have two equal pots. (Do most people?)

Do two inches of fresh water get you the same amount of H2O as two inches of salt water? Is this what we're trying to find out? Or is starting out with the same amount of H2O a prerequesite for answering a different question about what happens to the water later on?
Put the stills outside in the sun. Leave it [sic] alone for a few hours, or even a whole day. When you're ready, measure the water.
In inches?

And doesn't how long we leave them out affect the answer we get?

Assuming we even know what the question is...

Yes, I see now that communicating scientific ideas is very important. Perhaps we'll go with Option 3 next time.

Thursday, September 11, 2008

Math problems of the week: 6th grade Connected Math vs. Singapore Math

1. The first assignment in Connected Mathematics Prime Time: Factors and Multiples

My Special Number

Many people have a number they find interesting. Choose a whole number between 10 and 100 that you especially like.

In your journal
*record your number
*explain why you chose that number
*list three or four mathematical things about your number
*list three or four connections you can make between your number and your world

As you work through the investigations in Prime Time, you will learn lots of things about numbers. Think about how these new ideas apply to your special number, and add any new information about your number to your journal. You may want to designate one or two "special number" pages in your journal, where you can record this information. At the end of the unit, your teacher will ask you to find an interesting way to report to the class about your special number.

2. The first assignment in Singapore Mathematics Primary Mathematics 6A

A watermelon weighs m kg and a pineapple weights 2 kg.
(a) Express the total weight of the fruits in terms of m.


(b) if m = 4, find the total weight of the fruits.


(c) if m = 6, find the total weight of the fruits.

-----------

Apparently I'm in the minority: I don't have a favorite number. But I do have preferences within mathematics, and generally prefer algebra to number journaling.

If you have favorite numbers, or other mathematical preferences, please share them.

Tuesday, September 9, 2008

Using your analytical left brain to get out of Jury Duty

Usually a Ph.D. does it, but sometimes our city's courts are so desperate, or a particular panel of jurors too educated, for lawyers to peremptorily dismiss all those with advanced degrees. This was driven home to me several years ago when I served on my first jury.

A fascinating experience, particularly for me as a linguist.

But this time around, it was urgent that I get out, as I've just started teaching a graduate class for which there's no one who can substitute. While this doesn't constitute a "serious hardship," it was, in the end, this class that helped disqualify me. Among other things, I'm teaching conversational analysis--which includes, among other things, reading between the lines.

Things looked grim during the voir dire.  I had a low number--10 out of 40--and a half dozen others had already been dismissed.  But as soon as the judge asked me what I did as a linguist, my spirits soared.

Leaving out the other, more legally innocuous hats I wear, I replied, "I do pragmatics, which means I analyze conversations."

The judge looked bemused, and said, "You mean, you can tell me what I'm really thinking?"

"Exactly," I replied.

It took less than 5 seconds for them to dismiss me.

Friday, September 5, 2008

Earning high grades in Reform Math, II

I've just received my son's 6th grade homework guidelines, which include the following provisions about a particular homework contingency:

The "I Don't Understand It" Homework (receives full credit)

If you genuinely do not understand all or part of a problem, you must copy it completely, and explain in sentences what steps you took to try to do the problem. Write down the questions that you would ask me if I were with you. It is not enough to say, "I don't understand."

Please have your parent sign your homework. This signature is worth 1/2 pt extra credit!
These guidelines also require children who do understand the problems to explain their answers, and, though they don't say so explicitly, the protocol at our school is to deny full credit to unexplained answers, however correct. 

Thus, the math buff who can't be bothered to explain why 49 * 5 is 245 does worse than the math phobe who can't solve this problem but is happy to write down all his questions about how to do it.

Here's another question he might ask his teacher:  

When selecting a plumber or surgeon, do you pick someone who does the job well but refuses to explain how, or someone who articulately elaborates for you all the ways in which he or she is stumped?

Thursday, September 4, 2008

Math problems of the week: grade 2 Everyday Math vs. French math

A. The final multiplication word problems in the Everyday Math grade 2 Student Math Journal:


1. 3 vans full of people. How many people in all?

[picture of a van] vans people per van people in all
Holds 10 people ________ ___________ __________

Answer: ___ people
Number model: ___ X ___ = ____

2. 4 insects on the flower. How many legs in all?

[picture of a ladybug] insects legs per insect legs in all
Has 6 legs ________ __________ _________

Answer: ___ legs
Number model: ___ X ___ = ____

3. 9 windows, How many panes in all?

[picture of a window] windows panes per window panes in all
Has 4 panes ________ ___________ _________

Answer: ___ panes
Number model: ___ X ___ = ____

B. The sample grade 2 (CE 1) multiplication word problems from Professeur Phifix, a web resource for French curriculum materials (translated from the French):

For each problem, write down the calculation and a sentence as your answer.

Mr. Doudou wants to buy three armchairs for his vacation home. He decides not to spend more than 300 Euros. He goes to a store and finds armchairs at 35 euros each. He goes to another store and sees some for 28 euros, but these ones he doesn't like as much.

Can he buy the chairs from the first store, or must he buy those from the second store?

A person wants to take a 7 day trip to Greece. He goes to a travel agency which proposes to him a trip at 68 euros a day. The plane trip lasts 3 hours.

What is the total cost of this trip?

A school puts on a show to raise money for a computer. Tickets cost 6 euros. 234 people attend the show.

How much money was raised?

---------
Single digit by single digit multiplication and making students fill out forms

versus

single digit by multi-digit multiplication and letting students work things out on their own.

Tuesday, September 2, 2008

Summer projects, III: Not conforming to nonconformity

We've just completed the Literacy component of my son's summer projects, which includes:

Write a one-page, double spaced, Times New Roman discussion about the theme of conformity in Jerry Spinelli's Stargirl.  How do you feel about conformity?  Do you think it's important to act and dress like everyone else does?
From my autistic son's (one-page, double spaced, Times New Roman) response:
I think everybody should wear the same clothes and act normal, so people don't laugh at me.
I'm guessing that this isn't quite the response they were looking for. But my son is immune to pressures from teachers to conform to the expected bromides about the ills of nonconformity.

What grade this meta-nonconformity will earn him remains to be seen.